On a boundary control problem for a pseudo-parabolic equation

Farrukh Dekhkonov; Farrukh Dekhkonov

doi:10.3934/cam.2023015

Communications in Analysis and Mechanics

2023, Volume 15, Issue 2: 289-299. doi: 10.3934/cam.2023015

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On a boundary control problem for a pseudo-parabolic equation

Farrukh Dekhkonov ^,

Department of Mathematics, Namangan State University, Namangan, Uzbekistan

Received: 14 April 2023 Revised: 03 June 2023 Accepted: 13 June 2023 Published: 19 June 2023
35K70, 35K05

Previously, boundary control problems for parabolic type equations were considered. A portion of the thin rod boundary has a temperature-controlled heater. Its mode of operation should be found so that the average temperature in some region reaches a certain value. In this article, we consider the boundary control problem for the pseudo-parabolic equation. The value of the solution with the control parameter is given in the boundary of the interval. Control constraints are given such that the average value of the solution in considered domain takes a given value. The auxiliary problem is solved by the method of separation of variables, and the problem under consideration is reduced to the Volterra integral equation. The existence theorem of admissible control is proved by the Laplace transform method.
- Pseudo-parabolic equation,
- initial-boundary problem,
- admissible control,
- integral equation,
- Laplace transform
Citation: Farrukh Dekhkonov. On a boundary control problem for a pseudo-parabolic equation[J]. Communications in Analysis and Mechanics, 2023, 15(2): 289-299. doi: 10.3934/cam.2023015

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Abstract

Previously, boundary control problems for parabolic type equations were considered. A portion of the thin rod boundary has a temperature-controlled heater. Its mode of operation should be found so that the average temperature in some region reaches a certain value. In this article, we consider the boundary control problem for the pseudo-parabolic equation. The value of the solution with the control parameter is given in the boundary of the interval. Control constraints are given such that the average value of the solution in considered domain takes a given value. The auxiliary problem is solved by the method of separation of variables, and the problem under consideration is reduced to the Volterra integral equation. The existence theorem of admissible control is proved by the Laplace transform method.

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